Mr Biden was asked about Supreme Court packing and if he would support it.
That relates to the idea among some Democrats that if Mr Trump gets his nominee for the Supreme Court confirmed, Mr Biden should then expand the court to add two more justices if he's elected.
Mr Trump on Saturday nominated Amy Coney Barrett to the Supreme Court, picking a strong conservative to replace the late liberal justice Ruth Bader Ginsburg.
With Republicans almost certain to confirm Judge Barrett, Mr Trump will have been able to tilt the High Court to the right on the eve of his difficult re-election attempt.
Democrats have complained that Mr Trump should not be able to name a new justice so close to the presidential election.
Moderator Chris Wallace, a veteran political journalist from Fox News with a reputation for asking tough questions of both sides, interjected that the segment had ended.
"We've ended this segment," he said.
"That was a productive segment, wasn't it? Keep yapping man," Mr Biden said.
Earlier in the exchange Wallace kept asking Mr Trump to let Mr Biden finish what he was saying, with the President constantly cutting him off.
"He doesn't know how to do that," Mr Biden said.
"Please let him speak, Mr President," Wallace kept saying.